1. Lecture 20 Practical issues in motif finding Final project
CS5263 Bioinformatics
Lecture 20
Practical issues in motif finding
Final project

2. Motif representation Collection of exact words
{ACGTTAC, ACGCTAC, AGGTGAC, …}
Consensus sequence (with wild cards)
{AcGTgTtAC}
{ASGTKTKAC} S=C/G, K=G/T (IUPAC code)
Position specific weight matrices

3. Sequence Logo 1 2 3 4 5 6 7 8 9 A
.97
.10
.02
.03
.01
.05
.85 C
.40
.04 G
.95 .3 T
.90
.45 .6
.91 I
1.76
0.28
1.64
1.37
0.40
0.60
1.15
1.42

4. Finding Motifs

5. Phylogenetic footprinting
Motif finding schemes
Conservation
Yes No
Whole genome
Genome 1 & 2 & 3
Genome 1
Gene 1A & 1B & 1C or Gene Set 1 & 2 & 3
Gene Set 1
Phylogenetic footprinting
Dictionary building
“Motif finding” 1A 1B 1C
Gene set 1
Gene set 2
Gene set 3
Genome 1
Genome 2
Genome 3
Ideally, all information should be used, at some stage. i.e., inside algorithm vs pre- or post-processing.

6. Classification of approaches
Combinatorial search
Based on enumeration of words and computing word similarities
Analogy to DP for sequence alignment
Probabilistic modeling
Construct models to distinguish motifs vs non-motifs
Analogy to HMM for sequence alignment

7. Combinatorial motif finding
Given a set of sequences S = {x1, …, xn}
A motif W is a consensus string w1…wK
Find motif W* with “best” match to x1, …, xn
Definition of “best”:
d(W, xi) = min hamming dist. between W and a word in xi
d(W, S) = i d(W, xi)
W* = argmin( d(W, S) )

8. Exhaustive searches 1. Pattern-driven algorithm:
For W = AA…A to TT…T (4K possibilities)
Find d( W, S )
Report W* = argmin( d(W, S) )
Running time: O( K N 4K )
(where N = i |xi|)
Guaranteed to find the optimal solution.

9. Exhaustive searches 2. Sample-driven algorithm:
For W = a K-long word in some xi
Find d( W, S )
Report W* = argmin( d( W, S ) )
OR Report a local improvement of W*
Running time: O( K N2 )

10. Extended sample-driven (ESD) approaches
Hybrid between pattern-driven and sample-driven
Assume each instance does not differ by more than α bases to the motif ( usually depends on k)
motif
instance 
The real motif will reside in the -neighborhood of some words in S.
Instead of searching all 4K patterns, we can search the -neighborhood of every word in S.
α-neighborhood

11. WEEDER
Naïve: N Kα 3α NK
# of patterns to test
# of words in sequences

12. Better idea Using a joint suffix tree, find all patterns that:
Have length K
Appeared in at least m sequences with at most α mismatches
Post-processing

13. WEEDER: algorithm sketch
Current pattern P, |P| < K
A list containing all eligible nodes: with at most α mismatches to P
For each node, remember #mismatches accumulated (e), and bit vector (B) for seq occ, e.g. [ ]
Bit OR all B’s to get seq occurrence for P
Suppose #occ >= m
Pattern still valid
Now add a letter
A C G T T
# mismatches
(e, B)
Seq occ

14. WEEDER: algorithm sketch
Current pattern P
A C G T T A
Simple extension: no branches.
No change to B
e may increase by 1 or no change
Drop node if e > α
Branches: replace a node with its child nodes
Drop if e > α
B may change
Re-do Bit OR using all B’s
Try a different char if #occ < m
Report P when |P| = K
(e, B)

15. WEEDER: complexity Can get all D(P, S) in time
O(nN (K choose α) 3α) ~ O(nN Kα 3α).
n: # sequences. Needed for Bit OR.
Better than O(KN 4K) since usually α << K
Kα 3α may still be expensive for large K
E.g. K = 20, α = 6

16. WEEDER: More tricks Eligible nodes: with at most α mismatches to P
Current pattern P
A C G T T A
Eligible nodes: with at most α mismatches to P
Eligible nodes: with at most min(L, α) mismatches to P
L: current pattern length
: error ratio
Require that mismatches to be somewhat evenly distributed among positions
Prune tree at length K

17. MULTIPROFILER W differs from W* at  positions.
The consensus sequence for the words in the -neighborhood of W is similar to W.
If we ignore all the chars that are similar to W, the rest may suggest the difference between W and W* W* W
W*: ACGTACG
W: ATGTAAG

18. MULTIPROFILER: alg sketch
For each word P in S
Find its α-neighborhood in S
List of words: C
For each position j from 1..K of the words in C
Find the most popular char that differ from P[j]
Replace α positions in P with the chars found above
Call the new word P’
W* = argmin D(P’, S) W* W
W*: ACGTACG
W: ATGTAAG

19. MULTIPROFILER Complexity not discussed in the paper
More efficient than WEEDER for longer patterns: N < Kα 3α
How to choose α is an issue:
Large α: too many noises in neighborhood
Small α: few true instances in neighborhood W* W
W*: ACGTACG
W: ATGTAAG

20. Probabilistic modeling approaches
for motif finding

21. Probabilistic modeling approaches
A motif model
Usually a PWM
M = (Pij), i = 1..4, j = 1..k, k: motif length
A background model
Usually the distribution of base frequencies in the genome (or other selected subsets of sequences)
B = (bi), i = 1..4
A word can be generated by M or B

22. Expectation-Maximization
For any word W,
P(W | M) = PW[1] 1 PW[2] 2…PW[K] K
P(W | B) = bW[1] bW[2] …bW[K]
Let  = P(M), i.e., the probability for any word to be generated by M.
Then P(B) = 1 - 
Can compute the posterior probability P(M|W) and P(B|W)
P(M|W) ~ P(W|M) * 
P(B|W) ~ P(W|B) * (1-)

23. Expectation-Maximization
position 1 1
Initialize
E-step 5
probability 5 9 9
M-step
E-step: Zxy = P(M | X[y..y+k-1]) for all x and y
M-step: re-estimate M,  given Z

24. MEME Multiple EM for Motif Elicitation Bailey and Elkan, UCSD
Multiple starting points
Multiple modes: ZOOPS, OOPS, TCM

25. Gibbs Sampling
Another very useful technique for estimating missing parameters
EM is deterministic
Often trapped by local optima
Gibbs sampling: stochastic behavior to avoid local optima

26. Gibbs Sampling
position
probability
Sampling
Gibbs sampling: sample one position according to probability
Update prediction of one training sequence at a time
Viterbi: always take the highest
EM: take weighted average
Simultaneously update predictions of all sequences

27. Gibbs sampling motif finders
Gibbs Sampler, based on C. Larence et.al. Science, 1993
AlignACE, Nat Biotech 1998, developed in Church lab, Harvard Univ
BioProspector, X. Liu et. al. PSB 2001 , an improvement of AlignACE

28. Limits of Motif Finders
???
gene
Given upstream regions of coregulated genes:
Increasing length makes motif finding harder – random motifs clutter the true ones
Decreasing length makes motif finding harder – true motif missing in some sequences
Similar issue for number of sequences

29. Challenging problem (k, d)-motif challenge problem
d mutations
n = 20 k
L = 1000
(k, d)-motif challenge problem
Many algorithms fail at (15, 4)-motif for n = 20 and L = 1000
Combinatorial algorithms usually work better on challenge problems
However, they are usually designed to find (k, d)-motifs
Performance in real data varies

30. (15, 4)-motif Information content: 11.7 bits
~ 6mers. Expected occurrence 1 per 7k bp

31. Actual Results by MEME llr = 163 E-value = 3.2e+005

32. (15, 4’)-motif Motif length: 15
Each instance differs at most 4 bases from consensus
Information content: 14.8
Much easier problem

33. Actual
Results
by MEME
sites = 20     llr = 240     E-value = 4.7e-013
sites = 5     llr = 95     E-value = 1.8e+006
sites = 2     llr = 38     E-value = 3.0e+006

34. Results for some real genes
llr = 394     E-value = 2.0e-023
llr = 347     E-value = 9.8e-002
llr = 110     E-value = 1.4e+004

35. Motif finding in practice
Now we’ve found some good looking motifs
Easiest step?
What to do next?
Are they real?
How do we find more instances in the rest of the genome?
What are their functional meaning?
Motifs => regulatory networks

36. To make sense about the motifs
Each program usually reports a number of motifs (tens to hundreds)
Many motifs are variations of each other
Each program also report some different ones
Each program has its own way of scoring motifs
Best scored motifs often not interesting
AAAAAAAA
ACACACAC
TATATATAT

37. Strategies to improve results
Combine results from different algorithms usually helpful
Ones that appeared multiple times are probably more interesting
Except simple repeats like AAAAA or ATATATATA
Cluster motifs into groups according to their similarities

38. Strategies to improve results
Compare with known motifs in database
TRANSFAC
JASPAR
Issues:
How to determine similarity between motifs?
Alignment between matrices
How similar is similar?
Empirically determine some threshold

39. Strategies to improve results
Statistical test of significance
Enrichment in target sequences vs background sequences
Background set B
Target set T
Assumed to contain a common motif, P
Assumed to not contain P, or with very low frequency
Ideal case: every sequence in T has P, no sequence in B has P

40. Statistical test for significance
Background set + target set
B + T P
Target set T M N
Appeared in n sequences
Appeared in m sequences
Intuitively: if n / N >> m / M
P is enriched (over-represented) in T
Statistical significance?

41. Hypergeometric distribution
A box with M balls, of which N are red, and the rest are blue.
If we randomly draw m balls from the box
What’s the probability we’ll see n red balls?
If P is very small, we are probably not drawing randomly
Red ball: target sequences
Blue ball: background sequences
Total # of choices: (M choose m)
# of choices to have n red balls: (N choose n) x (M-N choose m-n)

42. Cumulative hypergeometric test for motif significance
We are interested in: if we randomly pick m balls, how likely that we’ll see at least n red balls?
This can be interpreted as the p-value for the null hypothesis that we are randomly picking.
Alternative hypothesis: our selection favors red balls.
Equivalent: the target set T is enriched with motif P.
Or: P is over-represented in T.

43. Examples Yeast genome has 6000 genes
Select 50 genes believed to be co-regulated by a common TF
Found a motif for these 50 genes
It appeared in 20 out of these 50 genes
In the whole genome, 100 genes have this motif
M = 6000, N = 50, m = = 120, n = 20
Intuition:
m/M = 120/6000. In Genome, 1 out 50 genes have the motif
N = 50, would expect only 1 gene in the target set to have the motif
20-fold enrichment
P-value = 6 x 10-22
n = 5. 5-fold enrichment. P-value = 0.003
Normally a very low p-value is needed, e.g

45. ROC curve for motif significance
Motif is usually a PWM
Any word will have a score
Typical scoring function: Log P(W | M) / P(W | B)
W: a word.
M: a PWM.
B: background model
To determine whether a sequence contains a motif, a cutoff has to be decided
With different cutoffs, you get different number of genes with the motif
Hyper-geometric test first assumes a cutoff
It may be better to look at a range of cutoffs

46. ROC curve for motif significance
Background set + target set
B + T P
Target set T M N
Given a score cutoff
Appeared in n sequences
Appeared in m sequences
With different score cutoff, will have different m and n
Assume you want to use P to classify T and B
Sensitivity: n / N
Specificity: (M-N-m+n) / (M-N)
False Positive Rate = 1 – specificity: (m – n) / (M-N)
With decreasing cutoff, sensitivity , FPR 

47. ROC curve for motif significance
A good cutoff 1
Lowest cutoff. Every sequence has the motif. Sensitivity = 1. specificity = 0.
ROC-AUC: area under curve.
1: the best. 0.5: random.
Motif 1 is more enriched in motif 2.
sensitivity
Motif 1
Motif 2
Random
1-specificity 1
Highest cutoff. No motif can pass the cutoff. Sensitivity = 0. specificity = 1.

48. Other strategies Cross-validation
Randomly divide sequences into 10 sets, hold 1 set for test.
Do motif finding on 9 sets. Does the motif also appear in the testing set?
Phylogenetic conservation information
Does a motif also appears in the homologous genes of another species?
Strongest evidence
However, will not be able to find species-specific ones

49. Other strategies Finding motif modules Location preference
Will two motifs always appear in the same gene?
Location preference
Some motifs appear to be in certain location
E.g., within bp upstream to transcription start
If a detect motif has strong positional bias, may be a sign of its function
Evidence from other types of data sources
Do the genes having the motif always have similar activities (gene expression levels) across different conditions?
Interact with the same set of proteins?
Similar functions?
etc.

50. To search for new instances
Usually many false positives
Score cutoff is critical
Can estimate a score cutoff from the “true” binding sites
Motif finding
Scoring function
A set of scores for the “true” sites. Take mean - std as a cutoff.
(or a cutoff such that the majority of “true” sites can be predicted).

51. To search for new instances
Use other information, such as positional biases of motifs to restrict the regions that a motif may appear
Use gene expression data to help: the genes having the true motif should have similar activities
Phylogenetic conservation is the key

52. Final project
Write a review paper on a topic that we didn’t cover in lectures Or
Implement an algorithm and do some experiments
Compare several algorithms (existing implementation ok)
Combine several algorithms to form a pipeline (e.g. gene expression + motif analysis)
Final:
5 -10 pages report (single space, single column, 12pt) + 15 minutes presentation

53. Possible topics for term paper
Haplotype inferencing
Computational challenges associated with new microarray technologies
Phylogenetic footprinting
Small RNA gene / target prediction (siRNA, mRNA, …)
Biomedical text mining
Protein structure prediction
Topology of biological networks

54. An example project Given a gene expression data (say cell cycle)
Cluster genes using k-means
Find motifs using several algorithms
(Cluster and combine similar motifs)
Rank motifs according to their specificity to the target sequences comparing to the other clusters
Get their logos
Use the sequences to search the whole genome for more genes with the motif
Do they have any functional significance?